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Mirrors > Home > MPE Home > Th. List > aev | Structured version Visualization version Unicode version |
Description: A "distinctor elimination" lemma with no restrictions on variables in the consequent. (Contributed by NM, 8-Nov-2006.) Remove dependency on ax-11 1930. (Revised by Wolf Lammen, 7-Sep-2018.) Remove dependency on ax-13 2101, inspired by an idea of BJ. (Revised by Wolf Lammen, 30-Nov-2019.) |
Ref | Expression |
---|---|
aev |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | aevlem1 2032 |
. . 3
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2 | ax6ev 1817 |
. . . 4
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3 | ax7 1870 |
. . . . 5
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4 | 3 | aleximi 1714 |
. . . 4
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5 | 2, 4 | mpi 20 |
. . 3
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6 | ax5e 1770 |
. . 3
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7 | 1, 5, 6 | 3syl 18 |
. 2
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8 | axc16g 2033 |
. 2
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9 | 7, 8 | mpd 15 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-12 1943 |
This theorem depends on definitions: df-bi 190 df-an 377 df-ex 1674 |
This theorem is referenced by: axc16nf 2037 axc16gALT 2206 2ax6e 2289 wl-naev 31906 wl-ax11-lem2 31960 |
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